The milk and water in two vessels are in the ratio of 3 : 1 and 7 : 11 respectively. In what ratio should the liquid in both the vessels be mixed to obtaina new mixture containing half milk and half water?

Step 1: Convert the given ratios into milk fractions

• Vessel A: Milk : Water = 3 : 1 → Milk fraction = 3 / (3 + 1) = 3/4 = 0.75
• Vessel B: Milk : Water = 7 : 11 → Milk fraction = 7 / (7 + 11) = 7/18 ≈ 0.3889
• Desired mixture: Milk and Water should be equal → Milk fraction = 0.5

Step 2: Apply alligation method

Vessel A (0.75)        Vessel B (0.3889)
      \                     /
       \                   /
     Mean milk = 0.5 (1:1)
       /                   \
      /                     \
0.5 - 0.3889 = 0.1111     0.75 - 0.5 = 0.25

Step 3: Calculate the ratio

Required ratio = 0.1111 : 0.25 ≈ 1111 : 2500 ≈ 4 : 9

Answer: 4 : 9

To achieve a final mixture containing equal parts of milk and water, the liquids from vessels A and B should be mixed in the ratio 4 : 9.